Determining status of electric power transmission lines in an electric power transmission system

ABSTRACT

The present application discloses systems and methods to determine loss of at least one electric power transmission line in an electric power transmission system. In various embodiments, a system consistent with the present disclosure may include an electrical parameter monitoring subsystem configured to receive electrical parameter measurements and to determine a change of the electrical measurements. An analysis subsystem may determine whether a change in the electrical measurements is indicative of loss of at least one transmission line and may calculate a number of transmission lines lost based on the change. In some embodiments, a remedial action subsystem may be configured to implement a remedial action in response to loss of at least one transmission line. The number of transmission lines lost may be determined based on an angle difference ratio and a power ratio between two buses in electrical transmission system.

RELATED APPLICATIONS

None

TECHNICAL FIELD

This disclosure relates to techniques that may be utilized to determinethe status of electric transmission lines in electric power transmissionsystems. More particularly, but not exclusively, the present disclosurerelates to systems and methods configured to detect loss of paralleltransmission lines based on a measured electric parameter between two ormore transmission buses and without reference to a fixed threshold.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments of the disclosure aredescribed, including various embodiments of the disclosure withreference to the figures, in which:

FIG. 1 illustrates an example of an embodiment of a simplified one-linediagram of an electric power delivery system with parallel transmissionlines consistent with embodiments of the present disclosure.

FIG. 2 illustrates a plot over time of an angle difference between thebuses in FIG. 1, before and after a transmission line is takenout-of-service consistent with embodiments of the present disclosure.

FIG. 3A illustrates a one-line diagram of an electric power deliverysystem with two transmission lines disposed between three transmissionbuses consistent with embodiments of the present disclosure.

FIG. 3B illustrates a graph over time showing an angle equal to adifference between the first transmission bus and the secondtransmission bus in the one-line diagram shown in FIG. 3A before andafter the transmission line between the first and second transmissionbuses is taken out-of-service.

FIG. 3C illustrates a graph over time showing an angle equal to adifference between the second transmission bus and the thirdtransmission bus in the one-line diagram shown in FIG. 3A before andafter the transmission line between the second and third transmissionbuses is taken out-of-service.

FIG. 4A illustrates a one-line diagram of an electric power deliverysystem with multiple connection paths disposed between threetransmission buses consistent with embodiments of the presentdisclosure.

FIG. 4B illustrates a graph showing a plot of an angle equal to adifference between the first transmission bus and the secondtransmission bus in the electric power delivery system illustrated inFIG. 4A.

FIG. 4C illustrates a graph over time showing an angle equal to adifference between the second transmission bus and the thirdtransmission bus in the electric power delivery system shown in FIG. 4A.

FIG. 5 illustrates a flow chart of a method for establishing adynamically adjustable threshold for detecting loss of a paralleltransmission line based on a standing angle difference between two busesconsistent with embodiments of the present disclosure.

FIG. 6 illustrates a flow chart of a method for detecting loss of atransmission line based on a measured electric parameter and withoutreference to a fixed tripping threshold.

FIG. 7 illustrates a function block diagram of an IED configured todetect loss of transmission lines in electric power transmission systemsconsistent with embodiments of the present disclosure.

In the following description, numerous specific details are provided fora thorough understanding of the various embodiments disclosed herein.However, those skilled in the art will recognize that the systems andmethods disclosed herein can be practiced without one or more of thespecific details, or with other methods, components, materials, etc. Inaddition, in some cases, well-known structures, materials, or operationsmay not be shown or described in detail in order to avoid obscuringaspects of the disclosure. Furthermore, the described features,structures, or characteristics may be combined in any suitable manner inone or more alternative embodiments.

DETAILED DESCRIPTION

In order to increase the reliability of electric power transmissionsystems, parallel transmission lines may be used. Parallel lines mayallow for transmission of electric power to continue while one of thelines is out-of-service. One of the lines may be taken out-of-serviceintentionally (e.g., to perform maintenance, repairs, or the like) ormay be taken out-of-service by an unplanned event (e.g., a weatherdisturbance, an accident, equipment failure, etc.). Delivery of electricpower may be interrupted in the event that both of the lines are takenout-of-service at the same time, whether the lines are takenout-of-service intentionally or unintentionally.

Detecting a loss of one of the parallel lines may be achieved using atleast two general techniques. First, the status of the line (e.g.,whether the line is in-service or out-of-service) may be determined bymonitoring the status of connecting devices (e.g., breakers, reclosers,etc). An indication of a status change may be communicated when aconnecting device changes state (e.g., changes from a closed orconducting state to an open state). Based on an analysis of suchconnecting devices, the status of a transmission line may be determined.Systems relying on state information to detect loss of a transmissionline may be referred to herein as state-based detection systems. Second,the status of a line may be determined by monitoring various electricparameters associated with the line, such as the voltage, current,and/or angle differences. Changes in such electric parameters mayprovide an indication that the status of the line has changed. Systemsrelying on measurements of electric parameters to detect loss of atransmission line may be referred to herein as measurement-baseddetection systems. Certain regulatory agencies may require that paralleltransmission lines be monitored using both a state-based detectionsystem and a measurement-based detection system. Use of both types ofsystems may improve the likelihood of detecting a change in the state ofthe parallel transmission lines.

Measurement-based detection systems may utilize voltage angle differenceschemes for detecting the loss of a parallel transmission line. Avoltage angle difference scheme may determine the relative angle betweentwo locations in the electric power transmission system. In certaininstances a static and preset angle difference threshold may bespecified for open line detection, which in turn results in selectivelydisconnecting power system assets (e.g., generators, loads, etc.) tomaintain stability of the system. Static and preset angle differencethreshold values may require study by an engineer to set appropriately.Further, such a threshold may be set too high to avoid false tripping,but thereby making the system slower to respond. Still further, staticand preset thresholds cannot dynamically adapt for changes in powerflow. In some circumstances, reliance on static and preset thresholdsmay not be sufficient to maintain transient stability in an electricpower transmission system.

Embodiments consistent with the present disclosure may be configured tomeet arbitrary critical clearing time requirements. Some embodimentsconsistent with the present disclosure may further be configured tooperate without the use of predetermined or static thresholds.Accordingly, such systems may avoid the need for engineering studiesaimed at identifying an appropriate threshold.

In various embodiments, a system consistent with the present disclosuremay monitor the currents flowing through parallel transmission linesconnecting two buses. The system may analyze the positive sequencevoltage angle (V1 angle) difference between the two buses. There couldbe a case where an external event might mislead the algorithm to take afalse decision. To avoid such cases and provide more security to thescheme, the algorithm will monitor the positive sequence currentmagnitudes to properly identify the switching event between the buses ofinterest. This current based condition can be used as arming logicbefore allowing the algorithm to declare open line condition. In onespecific embodiment, the arming logic may compare a positive sequencecurrent to a threshold. The threshold may be selected to be equal to orgreater than a minimum charging current of the line. In otherembodiments, the arming logic may calculate power ratios betweenparallel transmission lines, and may selectively enable the algorithmbased on changes in the monitored current ratio.

Also, since the algorithm assumes parallel transmission lines with sameline impedances, the currents measured at each end can be used to alarmfor an open line condition using current ratios. A change in currentratio between parallel transmission lines (with same impedance) can onlyoccur when one of the lines is taken out-of-service. This type of openline detection alarming may help operators of the electric powertransmission system to identify transmission lines that have been takenout-of-service.

In some embodiments a dynamically adjustable threshold-based approachmay be used. In such embodiments, a dynamically adaptable threshold maybe used to satisfy an arbitrary time requirement open line detection. Insuch embodiments, the dynamic adjustment of a threshold may be based onthe rate of change of angle difference or the rate of change of powerflow. As long as this rate of change is within a specified range, thethreshold may be moved proportionally to the increase in angledifference. If the rate of change exceeds the prescribed threshold, theangle difference threshold may remain static and may issue an open linedeclaration. In various embodiments, a standing angle difference may bemeasured and a constant margin above this level may be used as adetection threshold as long as the rate of change remains within anacceptable range.

Modern automation, electric power transmission, and distribution systemstypically include intelligent electronic devices (“IEDs”) forprotection, control, automation, and/or monitoring of equipment in thesystem. IEDs may be used to monitor equipment of many types, includingelectric transmission lines, electric distribution lines, currenttransformers, buses, switches, circuit breakers, reclosers,transformers, autotransformers, tap changers, voltage regulators,capacitor banks, generators, motors, pumps, compressors, valves, and avariety of other types of monitored equipment. In various embodimentsconsistent with the present disclosure, IEDs may be used in connectionwith the systems and methods disclosed herein.

Reference throughout this specification to “one embodiment” or “anembodiment” indicates that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment. Thus, the appearances of the phrases “in oneembodiment” or “in an embodiment” in various places throughout thisspecification are not necessarily all referring to the same embodiment.In particular, an “embodiment” may be a system, an article ofmanufacture (such as a computer readable storage medium), a method,and/or a product of a process.

The phrases “connected to,” “networked,” and “in communication with”refer to any form of interaction between two or more entities, includingmechanical, electric, magnetic, and electromagnetic interaction. Twocomponents may be connected to each other, even though they are not indirect physical contact with each other and even though there may beintermediary devices between the two components.

Some of the infrastructure that can be used with embodiments disclosedherein are already available, such as: general-purpose computers,computer programming tools and techniques, digital storage media, andoptical networks. A computer may include a processor such as amicroprocessor, microcontroller, logic circuitry, or the like. Theprocessor may include a special purpose processing device such as anASIC, PAL, PLA, PLD, Field Programmable Gate Array, or other customizedor programmable device. The computer may also include a computerreadable storage device such as: non-volatile memory, static RAM,dynamic RAM, ROM, CD-ROM, disk, tape, magnetic, optical, flash memory,or other computer readable storage medium.

The described features, operations, or characteristics may be combinedin any suitable manner in one or more embodiments. It will also bereadily understood that the order of the steps or actions of the methodsdescribed in connection with the embodiments disclosed herein may bechanged, as would be apparent to those skilled in the art. Thus, anyorder in the drawings or detailed description is for illustrativepurposes only and is not meant to imply a required order, unlessspecified to require an order.

In the following description, numerous details are provided to give athorough understanding of various embodiments. One skilled in therelevant art will recognize, however, that the embodiments disclosedherein can be practiced without one or more of the specific details, orwith other methods, components, materials, etc. In other instances,well-known structures, materials, or operations are not shown ordescribed in detail to avoid obscuring aspects of this disclosure.

FIG. 1 illustrates an example of an embodiment of a simplified one-linediagram of an electric power delivery system 100 with paralleltransmission lines 110 a, 110 b consistent with embodiments of thepresent disclosure. Electric power delivery system 100 may be configuredto generate, transmit, and distribute electric energy to loads. Electricpower delivery systems may include equipment, such as electricgenerators (e.g., generators 102 a, 102 b), power transformers (e.g.,transformers 104 a, 104 b), transmission lines (e.g., lines 110 a, 110b), circuit breakers (e.g., breakers 118 a, 118 b and 120 a, 120 b),busses (e.g., busses 106 a, 106 b) and the like. A variety of othertypes of equipment may also be included in electric power deliverysystem 100, such as voltage regulators, capacitor banks, loads, and avariety of other types of equipment that are not specificallyillustrated.

Electric power delivery system 100 may be monitored, controlled,automated, and/or protected using intelligent electronic devices (IEDs)112 a, 112 b. As used herein, an IED (such as IEDs 112 a, 112 b) mayrefer to any microprocessor-based device that monitors, controls,automates, and/or protects monitored equipment within system 100. Suchdevices may include, for example, remote terminal units, differentialrelays, distance relays, directional relays, feeder relays, overcurrentrelays, voltage regulator controls, voltage relays, breaker failurerelays, generator relays, motor relays, automation controllers, baycontrollers, meters, recloser controls, communications processors,computing platforms, programmable logic controllers (PLCs), programmableautomation controllers, input and output modules, and the like. The termIED may be used to describe an individual IED or a system comprisingmultiple IEDs.

IEDs 112 a, 112 b may communicate over various media such as a directcommunication link 114 or over a wide-area communications network (notshown). Communication link 114 may be facilitated by networking devicesincluding, but not limited to, multiplexers, routers, hubs, gateways,firewalls, and switches. In some embodiments, IEDs and network devicesmay comprise physically distinct devices. In other embodiments, IEDs andnetwork devices may be composite devices, or may be configured in avariety of ways to perform overlapping functions. IEDs and networkdevices may comprise multi-function hardware (e.g., processors,computer-readable storage media, communications interfaces, etc.) thatcan be utilized in order to perform a variety of tasks that pertain tonetwork communications and/or to operation of equipment within system100.

A common time signal may be distributed throughout system 100. The timesignal may be generated by multiple independent time sources, 124 a, 124b, 124 c or may be generated using a single time source. Time sources124 a, 124 b, 124 c may ensure that IEDs 112 a, 112 b have asynchronized time signal that can be used to generate time synchronizeddata, such as synchrophasors. The time signal may be distributed insystem 100 using a communications network or using a universal timesource, such as a global navigation satellite system, or the like.

IEDs 112 a, 112 b may monitor currents in transmission line 110 a usingcurrent transformers 122 a, 122 b, respectively; and IEDs 112 a, 112 bmay monitor currents in transmission line 110 b using currenttransformers 116 a, 116 b. IEDs 112 a, 112 b may utilize voltagetransformers 108 a, 108 b to monitor voltages on busses 106 a, 106 b.Consistent with various embodiments of the present disclosure, thevoltages and/or currents may be analyzed to determine the status of thetransmission lines 110 a, 110 b using various algorithms describedherein. Further, the voltages and/or currents may be communicated viacommunication link 114 for analysis from both sides of transmissionlines 110 a, 110 b. In the event of a loss of communication between IEDs112 a, 112 b, analysis may be limited to locally available informationgather by either IED 112 a or IED 112 b.

When one of the transmission lines 110 a, 110 b is removed from service,an angle difference between buses 106 a, 106 b may change. As describedin greater detail below, the angle difference between the buses mayinitially spike when one of the transmission lines 110 a, 110 b is takenout-of-service. Following the initial spike, the angle difference mayoscillate until settling at a new steady state value. Analysis of changein the angle may provide an indication that one of the transmissionlines 110 a, 110 b has been taken out-of-service. In electric powertransmission systems having two or more parallel transmission lines,analysis of the initial spike may be utilized to determine how manylines have been taken out-of-service between the two buses. When a lossof communication prevents transmission of data between IEDs 112 a, 112b, a determination that one of transmission lines 110 a, 110 b has beentaken out of service may be based on a change in the ratio of thecurrent flowing in the one transmission line to the current flowing inthe other transmission line.

The total real power transfer across the two parallel transmission linescan be represented mathematically using Eq. 1.

$\begin{matrix}{P = \frac{{V_{S}}*{V_{R}}*{\sin\left( {\delta_{S} - \delta_{R}} \right)}}{{jX}_{L}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$Where:

P is the power transmission value;

V_(S) is the voltage at the source terminal;

V_(R) is the voltage at the remote terminal;

δ_(S) is;

δ_(R) is; and,

X_(L) is the line reactance.

For a fixed power transmission value (P) and assuming that thetransmission lines 110 a, 110 b have the same impedance, if one paralleltransmission line is taken out-of-service, the line reactance jX_(L) isdoubled (assuming both the parallel lines have the same impedance).Accordingly, the angle must double to maintain the same power value.

FIG. 2 illustrates a plot 200 over time of an angle difference betweenthe buses 106 a, 106 b in FIG. 1, before and after a transmission lineis taken out-of-service consistent with embodiments of the presentdisclosure. The characterization and tracking of an initial jump 202following the loss of a transmission line at time 206 may be performedby measuring the rate of change of angle difference in a short timefollowing the loss of a parallel transmission line. Once the initialjump 202 occurs in the angle difference, the angle difference maycontinue to increase at a reduced rate of change 204. Determining acontinuing rise in the angle difference 204 may help to filter outtransients in angle difference measurement. In one specific embodiment,the initial jump may be characterized by a very high rate of change ofangle (or power flow). In one embodiment, the power flow may be inupwards/positive direction. For continuing rise, the rate of change ofangle (or power flow) is greater than zero but the rate itself is muchsmaller than the rate that we use to identify the initial spike. Forexample, the initial jump rate of change may exceed 300 degrees persecond and the continuing rate of change may exceed 20 degrees persecond. After reaching a maximum value, a period of oscillations 208 mayfollow before the oscillations settle to a new steady state value 210.

The angle difference before the start of the second rate of change 204along with the angle difference prior to the loss of the transmissionline at time 206 can be used to calculate an angle difference ratio. Theangle difference ratio, A_(R), is defined in Eq. 2.

$\begin{matrix}{A_{R} = \frac{\begin{matrix}{{Final}\mspace{14mu}{value}\mspace{14mu}{of}\mspace{14mu}{Angle}\mspace{14mu}{{diff} \cdot}} \\{{jump}\mspace{14mu}{immediately}\mspace{14mu}{after}\mspace{14mu}{the}\mspace{14mu}{event}}\end{matrix}}{{Angle}\mspace{14mu}{{diff} \cdot {before}}{\mspace{11mu}\;}{the}\mspace{14mu}{event}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$When the rate of change of the angle difference changes, the angledifference before and after the event may be determined. A power ratio,P_(R), which is defined in Eq. 3, may then be determined based on thenet power flow between the two buses before and after the event.

$\begin{matrix}{P_{R} = \frac{\mspace{14mu}\begin{matrix}{{Net}\mspace{14mu}{Power}\mspace{14mu}{flow}\mspace{14mu}{between}} \\{{the}\mspace{14mu}{two}\mspace{14mu}{buses}\mspace{14mu}{before}\mspace{14mu}{the}\mspace{14mu}{event}}\end{matrix}}{\begin{matrix}{{{Net}\mspace{14mu}{Power}\mspace{14mu}{Flow}\mspace{14mu}{between}\mspace{14mu}{the}\mspace{14mu}{two}}\mspace{11mu}} \\{{buses}\mspace{14mu}{immediately}\mspace{14mu}{after}\mspace{14mu}{the}\mspace{14mu}{event}}\end{matrix}\;}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$With the angle difference ratio and the real power ratio, the number ofparallel lines taken out-of-service may be determined. Morespecifically, the power ratio multiplied by the angle difference ratioprovides an indication of the change in the equivalent impedance as aresult of the loss of one or more transmission lines. This relationshipis set forth in Eq. 4.∥P _(R) *A _(R)∥=Number of Lines Lost  Eq. 4The result of Eq. 4 is an integer, since the number of transmissionlines lost is an integer.

FIG. 3A illustrates a one-line diagram of an electric power deliverysystem 300 with two transmission lines 304, 306 disposed between threetransmission buses 308, 310, 312 consistent with embodiments of thepresent disclosure. An equivalent source 302 is configured to generate aflow of electric current through transmission lines 304, 306 to beabsorbed by another equivalent source 314. Electric power deliverysystem 300 is a radial system with only one physical connection betweenbus 1 and bus 3 (i.e., serial transmission lines 304 and 306). In aradial system, such as electric power delivery system 300, if one of thetransmission lines is open, the current flow through the remaining linesbecome zero and it may be difficult to detect open line conditions foreach of the transmission lines. These difficulties, however, may beovercome using the systems and methods disclosed herein.

FIG. 3B illustrates a graph showing a plot of an angle 316 equal to adifference between a first transmission bus 308 and the secondtransmission bus 310 in the electric power delivery system 300 beforeand after transmission line 304 is taken out-of-service at time 314. Theangle difference wraps between −180° and 180°. The result indicates thattwo islands have formed and the power system has physically split intotwo segments.

FIG. 3C illustrates a graph over time showing an angle 318 equal to adifference between the second transmission bus 310 and the thirdtransmission bus 312 in the one-line diagram shown in FIG. 3A before andafter the transmission line 304 is taken out-of-service. As illustratedin FIG. 3C, the power across transmission line 306 becomes zero at time316 as a result of transmission line 304 being taken out-of-service.Typical low power/low current based detection schemes may fail undersuch a scenario for open line detection.

FIG. 4A illustrates a one-line diagram of an electric power deliverysystem 400 with multiple connection paths disposed between threetransmission buses 408, 410, 412 consistent with embodiments of thepresent disclosure. Generators 402, 404, 406 are configured to generatea flow of electric current through transmission lines 414, 416, 418,420. Electric power delivery system 400 is configured such that powermay be delivered to transmission buses 408, 410, 412 when one oftransmission lines 414, 416, 418, 420 is out-of-service.

FIG. 4B illustrates a graph showing a plot of an angle 426 equal to adifference between the first transmission bus 408 and the secondtransmission bus 410 in the electric power delivery system 400 beforeand after transmission line 414 is taken out-of-service at time 424. Theangle 426 increases because power is rerouted as a result oftransmission line 414 being taken out-of service. The transmission ofrerouted power through other connections in electric power deliverysystem 400 is going through a larger impedance. As described above, theincrease in the angle may be proportional to the increase in theimpedance resulting from transmission line 414 being takenout-of-service.

FIG. 4C illustrates a graph over time showing an angle 428 equal to adifference between the second transmission bus 410 and the thirdtransmission bus 412 in the electric power delivery system shown in FIG.4A before and after the transmission line between the second 410 andthird 412 transmission buses is taken out-of-service. As illustrated inFIG. 4C, the power across transmission line 416 becomes zero at time424. The topography of electric power delivery system 400, together withthe results shown in FIG. 4B and FIG. 4C may be used to determine thattransmission line 414 was taken out-of-service.

FIG. 5 illustrates a flow chart of a method 500 for establishing adynamically adjustable threshold for detecting loss of a paralleltransmission line based on a standing angle difference between two busesconsistent with embodiments of the present disclosure. At 502, electricparameter measurements associated with the first location may bereceived. Similarly, at 504, electric parameter measurements associatedwith a second location may be received. In various embodiments, theelectric parameter measurements may comprise voltage measurements,current measurements, angle measurements, power transfer measurements,etc. In some embodiments, two IEDs may be configured to acquire theelectric parameter measurements at different locations in an electricpower transmission system, and the measurements may be communicatedusing a data communication network. An exemplary configurationillustrating such a configuration is provided in FIG. 1 and describedabove. A standing angle difference may be determined between two busesin an electric power transmission system. The standing angle differencemay be a reflection of the amount of power transferred between the twobuses. Accordingly, as the power transferred between the two busesincreases, the standing angle difference may also increase. Similarly,as the power decreases, the standing angle difference may decrease.Although method 500 refers specifically to a standing angle differencebetween buses, one of skill in the art will recognize that method 500may be adapted for use in connection with other parameters.

At 506, the electric parameter measurements may be associated with timestamps. The time stamps may be generated by a receiving device or by adevice configured to acquire the measurements. As described below, inconnection with FIG. 7, certain IEDs may include a sensor componentconfigured to generate time-stamped measurements of various electricparameters. Further, such IEDs may be configured to communicate suchmeasurements with other devices to perform the various elementsassociated with method 500.

At 508, a maximum angle difference and rate of change of angledifference thresholds may be established that is suitable to maintainsystem stability. In other embodiments, the thresholds may be determinedin other ways. Further, at 510, an initial angle difference thresholdvalue may be established. In some embodiments, the threshold may dependon the time constrains needed to maintain transient stability in anelectric power transmission system. As described below, the thresholdvalue may be compared to the standing angle difference to determinewhether an open line condition should be declared. An acceptable rate ofchange range may be established for the standing angle differencebetween the buses. The acceptable rate of change range may be determinedby performing an analysis of a particular system. For example, aparticular system may be analyzed to determine a rate of change duringnormal loading and unloading conditions. Based upon the rate of changeduring normal conditions, a threshold may be established thatsubstantially exceeds the greatest rate of change during normalconditions. For example, the threshold may be set at two orders ofmagnitude higher than the rate of change experienced during normalconditions.

At 512, method 500 may determine whether a change in the electricparameter measurements is detected. In various embodiments, the electricparameter may be a standing angle difference between two paralleltransmission lines. Determination of the standing angle difference maybe performed using synchrophasors or other time-aligned data. The rateof change, in some embodiments, may be determined by comparing a currentvalue to prior value. In other embodiments, the rate of change may bedetermined with reference to some number of prior samples. If no changeis detected, method 500 may return to 502. If a change is detected, thechange may be analyzed to determine whether the change is indicative ofloss of at least one or more transmission lines.

At 514, method 500 may determine if the change does indicate loss of atleast one or more transmission lines. If not, at 522, method 500 maydetermine if any change to a dynamically adjusting angle differencethreshold is required. If so, the angle difference threshold is adjustedat 518, and the method returns to 510. If changes to the angledifference threshold are not required at 522, method 500 may return to508.

If method 500 determines at 514 that the change in electrical parametermeasurements are indicative of a loss of a transmission line, an openline condition may be declared at 516. In some embodiments, open linedeclaration may result in initiating a remedial action scheme (“RAS”) at520. The RAS may, for example, selectively disconnect or trip load orother components of the electric power transmission system to preservesystem stability. Further, the RAS may include reconfiguring theelectric power transmission system to re-route electric power around atransmission line that has been taken out-of-service. In still otherembodiments, the remedial action may include initiating an alarmcondition that notifies operators of the electric power transmissionsystem of the open line condition. In various embodiments, determinationof the standing angle may be performed using synchrophasors or othertime-aligned data. The rate of change, in some embodiments, may bedetermined by comparing a current value to prior value. In otherembodiments, the rate of change may be determined with reference to somenumber of prior samples.

The following example illustrates one embodiment of a dynamicallyadjustable threshold-based system consistent with the presentdisclosure. In the system, a standing angle difference of 2 degreesbetween two parallel transmission lines correspond to 900 MW of typicalpower transfer at 400 kV. In the system, power transfer may rangeanywhere between 0 to 2000 MW. A power transfer of 1800 MW in the systemwould result in a standing angle difference of 4 degrees (assuming therewere no change in impedance and no significant change in voltagemagnitudes). To satisfy stability constraints a tripping scheme mustoperate in less than 100 milliseconds. A field test measured that asynchrophasor-based angle difference element set to 4 degrees hasoperated in 92 milliseconds whereas an angle difference element set to 5degrees for the same event has operated in 292 milliseconds.

Based on the parameters of the example set forth in the precedingparagraph, a threshold of 4 degrees cannot be used as it is within therange of typical power flow over that network and a threshold of 5degrees cannot guarantee the system stability because the element wouldoperate too slowly. Accordingly, a system consistent with the presentdisclosure may establish a dynamically adjustable threshold. For a powerflow of 900 MW, the angle difference tripping element may dynamicallyset the threshold to be 4 degrees. As the power flow gradually increasesto 1800 MW, the angle difference threshold will be gradually moved fromits current threshold maintaining the same ratio between the angledifference and the power transfer.

FIG. 6 illustrates a flow chart of a method 600 for detecting loss of atransmission line based on a measured electric parameter and withoutreference to any detection threshold. At 602, electric parametermeasurements associated with a first location may be received.Similarly, at 604, electric parameter measurements associated with asecond location may be received. In various embodiments, the electricparameter measurements may comprise voltage measurements, currentmeasurements, angle measurements, power transfer measurements, etc. Insome embodiments, two IEDs may be configured to acquire the electricparameter measurements at different locations in an electric powertransmission system, and the measurements may be communicated using adata communication network. An exemplary configuration illustrating sucha configuration is provided in FIG. 1 and described above.

At 606, the electric parameter measurements may be associated with timestamps. The time stamps may be generated by a receiving device or by adevice configured to acquire the measurements. As described below, inconnection with FIG. 7, certain IEDs may include a sensor componentconfigured to generate time-stamped measurements of various electricparameters. Further, such IEDs may be configured to communicate suchmeasurements with other devices to perform the various elementsassociated with method 600.

At 608, method 600 may determine whether a change in the electricparameter measurements is detected. If no change is detected, method 600may return to 602. If a change is detected, the change may be analyzedto determine whether the change is indicative of a loss of one or moretransmission lines. As discussed above in connection with FIG. 2, aninitial jump in a standing angle difference between two points in anelectric transmission system followed by a continued rise in thestanding angle difference may be an indication that a transmission linehas been taken out-of-service. On the other hand, however, as describedin connection with FIG. 5, where a rate of change in the electricalparameters is relatively small, the change may simply reflect changingconditions within the loading/unloading conditions of the electric powertransmission system.

When method 600 determines that the change in electrical parameters isindicative of the loss of a transmission line at 609, the number oftransmission lines taken out-of-service and which specific transmissionlines were taken out-of-service may be determined at 610. As describedabove, Eqs. 1-4 may be solved to determine the number of lines takenout-of-service. Further, as described in connection with FIGS. 3A-3C andFIGS. 4A-4C the response of the electric power transmission system andthe topography of the system may be analyzed to identify the specifictransmission lines that were taken out-of-service. If the change inelectrical parameters is not indicative of the loss of a transmissionline at 609, method 600 may return to 602.

At 612, open line condition may be declared and remedial action may beinitiated at 614. In some embodiments, open line declaration may resultin initiating a RAS controller that selectively disconnects loads orother components of the electric power transmission system to preservesystem stability. Further, remedial action may include reconfiguring theelectric power transmission system to re-route electric power around atransmission line that has been taken out-of-service. In still otherembodiments, the remedial action may include initiating an alarmcondition that notifies operators of the electric power transmissionsystem.

FIG. 7 illustrates a function block diagram of an IED 700 configured todetect loss of transmission lines in electric power transmission systemsconsistent with embodiments of the present disclosure. IED 700 may beconfigured to perform a variety of tasks using a configurablecombination of hardware, software, firmware, and/or any combinationthereof. The subsystems illustrated in FIG. 7 may be embodied ashardware using, for example, embedded systems, field programmable gatearray implementations, and specifically designed integrated circuits.The subsystems illustrated in FIG. 7 may also be embodied using acombination of hardware and software. More specifically, a generalpurpose processor and a plurality of software modules may be configuredto perform the various features and functions described herein.Moreover, certain components or functions described herein may beassociated with other devices or performed by other devices. Thespecifically illustrated configuration is merely representative of oneembodiment consistent with the present disclosure.

IED 700 includes a network communications interface 716 configured tocommunicate with other IEDs and/or system devices. In certainembodiments, the network communications interface 716 may facilitatedirect communication with another IED or communicate with another IEDover a communications network. The network communications interface 716may facilitate communications with multiple IEDs. IED 700 may furtherinclude a time input 712, which may be used to receive a time signalallowing IED 700 to apply a time-stamp to the acquired samples. Incertain embodiments, a common time reference may be received viacommunications interface 716, and accordingly, a separate time input maynot be required for time-stamping and/or synchronization operations. Onesuch embodiment may employ the IEEE 1588 protocol. A monitored equipmentinterface 708 may be configured to receive status information from, andissue control instructions to, a piece of monitored equipment. Suchequipment may include, for example, breakers, reclosers, or otherdevices configured to selectively connect or disconnect a portion of anelectric power transmission system.

A local communication interface 706 may also be provided for localcommunication with IED 700. The local communication interface 706 may beembodied in a variety of ways, including as a serial port, a parallelport, a Universal Serial Bus (USB) port, an IEEE 1394 Port, and thelike.

In certain embodiments, IED 700 may include a sensor component 710. Inthe illustrated embodiment, sensor component 710 is configured to gatherdata directly from a plurality of conductors 714 a-c and may use, forexample, A/D converters 718 that may sample and/or digitize filteredwaveforms to form corresponding digitized current and voltage signalsprovided to data bus 722. Conductors 714 a-c may be electricallyconnected to an electric power transmission system. In some embodimentstransformers (not shown) may reduce the voltage or current to a levelappropriate for monitoring using the IED 700. A/D converters 718 mayinclude a single A/D converter or separate A/D converters for eachincoming signal. A current signal may include separate current signalsfrom each phase of a three-phase electric power system. A/D converters718 may be connected to processor 724 by way of data bus 722, throughwhich representations of electric parameters determined by sensorelements 702 a-c may be transmitted to processor 724. In variousembodiments, the representations of electric parameters may representparameters, such as currents, voltages, frequencies, phases, and otherparameters associated with an electric power transmission system. Sensorelements 702 a-c may represent a variety of types of elements, such asvoltage transformers, current transformers, status inputs, a breakercontroller, etc.

Processor 724 may be configured to process communications received viacommunications interface 716, time input 712, monitored equipmentinterface 708, and/or sensor component 710. Processor 724 may operateusing any number of processing rates and architectures. Processor 724may be configured to perform various algorithms and calculationsdescribed herein. Processor 724 may be embodied as a general purposeintegrated circuit, an application specific integrated circuit, afield-programmable gate array, and/or any other suitable programmablelogic device.

An electric parameter monitoring subsystem 738 may be configured tomonitor specified electric parameters and to determine whether a changein the electric monitored parameters is detected. In variousembodiments, the electric parameters may be received directly fromsensor component 710. In other embodiments, the parameters may bereceived via the network communication interface 716, the monitoredequipment interface 708 or the local communication interface 706.

When a change is detected by the electric parameter monitoring subsystem738, the analysis subsystem 730 may be configured to analyze the changesto determine whether the changes indicate that one or more transmissionlines have been taken out-of-service. In one specific embodiment,analysis subsystem 730 may be configured to solve Eqs. 1-4 to determinea number of lines taken out-of-service. Further, as described inconnection with FIGS. 3A-3C and FIGS. 4A-4C the response of the electricpower transmission system and the topography of the system may beanalyzed to identify the specific transmission lines that were takenout-of-service. Topography subsystem 734 may be configured to provideinformation relating to the topography of an electric power transmissionsystem to aid in the determination of which transmission line has beentaken out-of-service.

A remedial action subsystem 732 may be configured to implement one ormore actions in response to a determination that one or moretransmission lines have been taken out-of-service. Specifically,remedial action subsystem 732 may be configured to selectivelydisconnect loads or other components of the electric power transmissionsystem to preserve system stability. Further, remedial action subsystem732 may, in conjunction with topography subsystem 734, reconfigure theelectric power and transmission system to re-route electrical poweraround a transmission line that has been taken out-of-service. In stillother embodiments, remedial action subsystem 732 may initiate an alarmthat notifies operators of the electric power transmission system that atransmission line has been taken out-of-service.

A threshold adjustment subsystem 736 may be configured to establish andadjust a dynamic threshold that may be used for detecting loss of atransmission line. In one specific embodiment, threshold adjustmentsubsystem 736 may be configured to implement the specific methodillustrated in FIG. 5 and described in detail above.

The above description provides numerous specific details for a thoroughunderstanding of the embodiments described herein. However, those ofskill in the art will recognize that one or more of the specific detailsmay be omitted, or other methods, components, or materials may be used.In some cases, operations are not shown or described in detail.

While specific embodiments and applications of the disclosure have beenillustrated and described, it is to be understood that the disclosure isnot limited to the precise configuration and components disclosedherein. Various modifications, changes, and variations apparent to thoseof skill in the art may be made in the arrangement, operation, anddetails of the methods and systems of the disclosure without departingfrom the spirit and scope of the disclosure.

What is claimed:
 1. A system configured to determine loss of at leastone electric power transmission line in an electric power transmissionsystem, the system comprising: an electrical parameter monitoringsubsystem configured to: receive a first plurality of electricalparameter measurements taken at a first location over a period of time;receive a second plurality of electrical parameter measurements taken ata second location over the period of time; and determine a change in thefirst plurality of electrical measurements and the second plurality ofelectrical measurements over the period of time; an analysis subsystemconfigured to: determine that the change is indicative of loss of atleast one transmission line; calculate an angle difference ratio;calculate a power ratio; and calculate a number of transmission lineslost by calculating a product of the angle difference ratio and thepower ratio; and a remedial action subsystem configured to implement aremedial action in response to loss of at least one transmission line,the remedial action comprising one of reconfiguring the electric powertransmission system to re-routing electric power around the at least onetransmission line and selectively disconnecting a load.
 2. The system ofclaim 1, wherein the analysis subsystem is further configured to:identify an initial increase in at least one of the first plurality ofelectrical parameter measurements and the second plurality of electricalparameter measurements; and identify a continuing increase following theinitial increase at a reduced rate of change to determine that thechange is indicative of loss of at least one transmission line.
 3. Thesystem of claim 1, wherein the analysis subsystem is configured todetermine that the change is indicative of loss of at least onetransmission line without reference to a static threshold.
 4. The systemof claim 1, wherein the electrical parameter monitoring subsystem isfurther configured to: measure a first current flowing in a firsttransmission line; measure a second current flowing in a secondtransmission line with an impedance that is approximately equal to animpedance of the first transmission line; and identify a change in aratio of the first current to the second current.
 5. The system of claim4, wherein the analysis subsystem is further configured to initiate asecond remedial action based on loss of communication with the secondlocation and based on the change in the ratio of the first current tothe second current.
 6. The system of claim 1, further comprising acommunication interface configured to receive at least one of the firstplurality of electrical parameter measurements and the second pluralityof electrical parameter measurements.
 7. The system of claim 1, furthercomprising a sensor component configured to measure at least one of thefirst plurality of electrical parameter measurements and the secondplurality of electrical parameter measurements.
 8. The system of claim7, further comprising a time input configured to receive a time signaland wherein each of the plurality of electric parameter measurementsmade by the sensor component is associated with a time-stamp.
 9. Thesystem of claim 1, wherein the first location and the second locationremain in electrical communication after the loss of the at least onetransmission line.
 10. A method of determining loss of at least oneelectric power transmission line in an electric power transmissionsystem, the method comprising: receiving a first plurality of electricalparameter measurements taken at a first location over a period of time;receiving a second plurality of electrical parameter measurements takenat a second location over the period of time; determining a change inthe first plurality of electrical measurements and the second pluralityof electrical measurements over the period of time; determining that thechange is indicative of loss of at least one transmission line;calculating an angle difference ratio; calculating a power ratio;calculating a number of transmission lines lost by calculating a productof the angle difference ratio and the power ratio; declaring an openline condition; and initiating a first remedial action, the firstremedial action comprising one of reconfiguring the electric powertransmission system to re-routing electric power around the at least onetransmission line and selectively disconnecting a load.
 11. The methodof claim 10, wherein determining that the change is indicative of lossof at least one transmission line comprises: identifying an initialincrease in at least one of the first plurality of electrical parametermeasurements and the second plurality of electrical parametermeasurements; identifying a continuing increase following the initialincrease at a reduced rate of change.
 12. The method of claim 10,further comprising: identifying a specific transmission line lost byanalyzing the first plurality of electrical parameter measurements, thesecond plurality of electrical parameter measurements, and thetopography of the electric power transmission system.
 13. The method ofclaim 10, wherein determining that the change is indicative of loss ofat least one transmission line is performed without reference to astatic threshold.
 14. The method of claim 10, wherein determining thatthe change is indicative of loss of at least one transmission linecomprises: measuring a first current flowing in a first transmissionline; measuring a second current flowing in a second transmission linehaving an impedance that is approximately equal to an impedance of thefirst transmission line; and identifying a change in a ratio of thefirst current to the second current.
 15. The method of claim 14, furthercomprising: losing communication with the second location; initiating asecond remedial action based on the change in the ratio of the firstcurrent to the second current.